# Determine the validity of the number problem

• chwala
So, in summary, the marking scheme indicates that the answer is ##38=31+7## only for the even number 38. This is because 38 is the only even number that can be expressed as the sum of two prime numbers in only one way, while all other even numbers between 30 and 50 can be expressed in two different ways. This makes the claim that all even numbers can only be expressed in one way false, with 38 being the counterexample. This is due to the fact that the prime numbers 7 and 31 are the only two numbers that can add up to 38 without any other combination possible.
chwala
Gold Member
Homework Statement
ii. Find a number between ##30## and ##50##which shows the statement is false.
Relevant Equations
numbers

my question is on part ii. Only,

the marking scheme indicates that the answer is ##38=31+7## only. My question is why is this False? ##38## is an even number, ##7## and ##31## are two different prime numbers and their sum gives us ##38##!
i would say##32=13+17+2##
##31=13+17+1##

which is false, ooooh! unless the value indicated above is only true for value ##38## and not any other value between ##30## and ##50##. English was a problem there...

Delta2
It says it needs to be summed in two different ways. For example 16=11+5 and also 16=13+3, you need two different sums of two primes.

Delta2 and chwala
Office_Shredder said:
It says it needs to be summed in two different ways. For example 16=11+5 and also 16=13+3, you need two different sums of two primes.
Aaargh I see that now...thanks

chwala said:
Aaargh I see that now...thanks
##32=29+3=13+19##

So 32 it's not a counterexample. The claim is you can do this for all even numbers, and the solution says that 38 is the counterexample.

chwala
I agree,I understand now...its very clear. The claim is false because of ##38## as you have clearly shown...Thank you once again...

Office_Shredder said:
So 32 it's not a counterexample. The claim is you can do this for all even numbers, and the solution says that 38 is the counterexample.
True, whereas in the even numbers like
##32= 3+29 = 13+19## [3 to 13 (+10)...therefore for 29 (-10) = 19]
##34=5+29 = 11+23## [5 to 11 (+ 6)...therefore for 29 ( -6) = 23]

Now the number ##38## can only be expressed in the form ##38= 7+31## and no any other combination.

## What is the meaning of a "valid" number problem?

A valid number problem is one that has a correct and logical solution. It follows the rules and principles of mathematics and can be solved using appropriate methods and operations.

## How do you determine the validity of a number problem?

To determine the validity of a number problem, you need to carefully analyze the problem and its given conditions. Then, you can use mathematical principles and operations to solve the problem and check if the solution is correct and logical.

## What are some common mistakes that can make a number problem invalid?

Some common mistakes that can make a number problem invalid include using incorrect mathematical operations, misinterpreting the given conditions, and making calculation errors.

## Can a number problem have multiple valid solutions?

Yes, a number problem can have multiple valid solutions. This can happen when there are different ways to interpret the given conditions or when the problem allows for more than one correct answer.

## How can you ensure the validity of your solution to a number problem?

To ensure the validity of your solution to a number problem, you can double-check your calculations and make sure they follow the correct mathematical principles. You can also try solving the problem using different methods to verify your answer.

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